docs: def V_vertical_ellipsoidal_concave(D, a, h):
      r'''Calculates volume of a vertical tank with a concave ellipsoidal bottom,
      according to [1]_. No provision for the top of the tank is made here.
  
      .. math::
          V = \frac{\pi D^2}{12} \left(3h + 2a - \frac{(a+h)^2(2a-h)}{a^2}\right)
          ,\;\; 0 \le h < |a|
  
      .. math::
          V = \frac{\pi D^2}{12} (3h + 2a ),\;\; h \ge |a|
  
      Parameters
      ----------
      D : float
          Diameter of the main cylindrical section, [m]
      a : float
          Negative distance the eppilsoid head extends inside the main cylinder, [m]
      h : float
          Height, as measured up to where the fluid ends, [m]
  
      Returns
      -------
      V : float
          Volume [m^3]
  
      Examples
      --------
      Matching example from [1]_, with inputs in inches and volume in gallons.
  
      >>> V_vertical_ellipsoidal_concave(D=113., a=-33, h=15)/231
      44.84968851034856
  
      References
      ----------
      .. [1] Jones, D. "Compute Fluid Volumes in Vertical Tanks." Chemical
         Processing. December 18, 2003.
         http://www.chemicalprocessing.com/articles/2003/193/
      '''
      if h < abs(a):
          Vf = pi*D**2/12.*(3*h + 2*a - (a+h)**2*(2*a-h)/a**2)
      else:
          Vf = pi*D**2/12.*(3*h + 2*a)
      return Vf